Answer:
(4, -18)
Step-by-step explanation:
First Use this formula for the x -axis -b/2a
-8/2(1) is -4
Then plug in -4 to the equation
(-4)^2+8(-4)-2 = -18
For the first problem the answer is -5/2
2x−7+10=−2
Step 1: Simplify both sides of the equation.
2x−7+10=−2
2x+−7+10=−2
(2x)+(−7+10)=−2
(Combine Like Terms)
2x+3=−2
Step 2: Subtract 3 from both sides.
2x+3−3=−2−3
2x=−5
Step 3: Divide both sides by 2.
2x/2=−5/2
x=−5/2
Answer:
x= -5/2
→ 6x² - 2x - 20
→ 6x² + 10x - 12x - 20
→ x(6x + 10 ) - 2 (6x + 10)
→ (6x + 10) (x - 2) .
for
6x - 10 = 0
6x = 10
for x - 2
x = 2
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
